There are many applications in the processing of data in which filtering is required. For example, where data originally recorded at a first sampling rate is to be subsampled at a less frequent rate to save storage space and reduce subsequent processing costs, low pass filtering is commonly performed prior to the resampling step to avoid aliasing in the resultant record. Filtering is also performed to remove sinusoidal noise from the data. For example, if seismic exploration is carried out in the vicinity of a generator or power line, frequently the data will be corrupted by 60 Hz noise and harmonics thereof, which can be a great impediment in reading the data records. There are numerous other sources of noise as well. For example, source generated noise, i.e., waves of seismic energy from the source, often obscures the desired seismic reflection signals. In the marine environment, acoustic noise from a multitude of sources (i.e., the towing ship, the tailbuoy at the end of the "streamer", depth-controlling "birds" on the streamer, etc.) is commonly detected by the hydrophones and recorded. Noise from these sources often occupies well-defined frequency bands and must be removed from the recorded data before interpretation is possible.
This invention relates to improved methods of removing such band-limited noise from data.
More particularly, in seismic exploration of the earth for oil, gas and other valuable minerals, the usual practice is to impart energy into the earth at a "shot point". This can be done on land by detonating a charge of dynamite, or shaking a heavy weight and coupling the energy into the earth. In water-based exploration, this is done by releasing a "shot" of compressed air into the water. In each case, the energy travels downwardly into the earth, is reflected at interfaces between rock layers, and returns upwardly, where it can be detected by geophones (on land) or by hydrophones (in the water). Output signals from the detectors, or "traces", are recorded as functions of time, and the shapes of the "wiggles" in them analyzed to determine the shape of the reflectors within the earth. The shapes of the reflectors are then analyzed by geophysicists in their search for valuable minerals.
The fact that the seismic energy must travel deeply into the earth and return necessarily means that the signals which are to be detected are quite weak and can readily be obscured by noise. Accordingly, a great deal of attention has been paid to the removal of noise from seismic records. However, further improvements are still needed. Even where a particular method may yield useful results, it is of substantial utility to reduce the time necessary to process the data accordingly, as such processing steps can be very expensive. It is also of substantial utility to minimize the computational effort required to design suitable filters.
It will be appreciated by those of skill in the art that certain types of random noise often found in seismic records can be removed from seismic records by "stacking", that is, by summing together comparable traces in which the noise is essentially random. Because the noise is random while the signals are correlated, the signal-to-noise ratio can be improved by the stacking process. However, if the noise occupies an identifiable frequency band which differs from the frequency of the seismic energy, a much greater improvement is obtained by first filtering the data traces to remove the noise.
As indicated above, a common source of noise corrupting seismic records is noise from known sources. While the art teaches methods of removing such noise from records, the methods proposed in the prior art have normally involved digital filtering using relatively long operators to remove the noise from the data records. Such techniques are quite expensive, as the operators involve numerous coefficients which must be multiplied by the individual digital samples of the traces. Thus, the cost of such operations goes up with the number of coefficients. In many cases, the cost is so high that the noise is simply ignored and the geophysicist is obliged to read the data despite the presence in the record of noise of known frequency content, which could be removed if an adequate method were provided for doing so.
The art also teaches the use of notch filters for removal of sinusoidal noise from signals. However, the art has typically not implemented these in a way which is truly useful.
In U.S. Pat. No. 4,853,903 issued to the present inventors and a third inventor on Aug. 1, 1989, (hereinafter "the '903 patent") there is disclosed a method for removing one or more sinusoidal noise components from a seismic record. This patent is not prior art to the instant application, but is incorporated herein by reference. In the '903 patent, an individual trace of a set of data traces is analyzed to determine the frequency of the interfering sinusoidal noise by Fourier transformation thereof. A digital notch filter is constructed using the exact autocorrelation function of the sinusoidal noise. The notch filter is then convolved with the data trace thus removing the sinusoidal noise from the signal.
The present invention comprises a further improvement and refinement of the techniques shown in the '903 patent.